Free · Physics models
Electron Speed after an Accelerating Voltage
Compare classical and relativistic electron speed for an electron starting at rest across a positive accelerating potential.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
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Formula and method
newton v = 18755.373 kmps; real v = 18727.897 kmps.
vNewton = √(2eV/m); vRel = c√[1 − (1+eV/mc²)⁻²].
Worked example
Enter these known values and leave the other values blank.
- Accelerating potential
- 1000 V
- Classical velocity
- 18755 km/s
- Relativistic velocity
- 18728 km/s
- Velocity difference
- -27.5 km/s
Assumptions and limitations
- Compare classical and relativistic electron speed for an electron starting at rest across a positive accelerating potential.
- This captured comparison uses e = 1.60217662×10⁻¹⁹ C, m = 9.10938356×10⁻³¹ kg, rest energy 8.1871057769×10⁻¹⁴ J and exact c. These are retained historical approximations rather than current precision constants.
- Classical speed can exceed c at sufficiently high voltage; it illustrates approximation failure. The relativistic result remains below c for finite positive voltage.
- Inputs and inverse outputs share the displayed unit selectors. Clear a known field to solve for it, and lock quantities that must remain fixed. Singular inverses may have no finite result.
Common questions
Why do the answers differ?
Classical kinetic energy is inadequate as speed approaches light speed; relativistic energy includes the Lorentz factor.
Does this include initial speed?
No. The model starts from rest and omits collisions and radiation losses.
References
Compare classical and relativistic electron speed for an electron starting at rest across a positive accelerating potential. This captured comparison uses e = 1.60217662×10⁻¹⁹ C, m = 9.10938356×10⁻³¹ kg, rest energy 8.1871057769×10⁻¹⁴ J and exact c. These are retained historical approximations rather than current precision constants. Classical speed can exceed c at sufficiently high voltage; it illustrates approximation failure. The relativistic result remains below c for finite positive voltage.